Remark. Notice that the notion of weak Carmichael numbers was introduced in the article by Romeo Meˇstrovi´c, Generalizations of Carmichael numbers I, preprint arXiv:1305.1867v1 [math.NT], 4 May 2013, 46 pages. Accordingly, a composite positive integer n is said to be a weak Carmichael number if X k n−1 ≡ ϕ(n) (mod n), gcd(k,n)=1 1≤k≤n−1
where gcd(k, n) denotes the greatest common divisor of k and n, and ϕ(n) is the Euler totient function, defined as the number of positive integers less than n which are relatively prime to n. The above Table 1 was given as Table 1 on page 15 in the previously mentioned paper. Table 1 shows that there are 102 weak Carmichael numbers less than 25000, and between them there are 9 Carmichael numbers, 57 odd prime powers and 36 other composite numbers. In bold are assigned Carmichael numbers. Recall that in 2006 R.G.E. Pinch (The Carmichael numbers up to 1
2
1018 ; preprint arXiv:math/0604376v1 [math.NT], 2006) reported that there are 1401644 Carmichael numbers up to 1018 .